Automation of the Procedure for Filling Matrices of Pairwise Comparison of Alternatives by Criteria when using the Analytic Hierarchy Process

2019 ◽  
Vol 25 (6) ◽  
pp. 331-339
Author(s):  
Nefedov A. S. ◽  
◽  
V. A. Shakirov ◽  
Keyword(s):  
Analytic Hierarchy Process ◽  
Pairwise Comparison ◽  
Analytic Hierarchy ◽  
The Analytic Hierarchy Process ◽  
Hierarchy Process

JUDGMENT NUMBER REDUCTION: AN ISSUE IN THE ANALYTIC HIERARCHY PROCESS

2010 ◽  
Vol 09 (01) ◽  
pp. 175-189 ◽  
Author(s):  
LONG-TING WU ◽  
XIA CUI ◽  
RU-WEI DAI
Keyword(s):  
Decision Making ◽  
Analytic Hierarchy Process ◽  
Pairwise Comparison ◽  
Random Variable ◽  
Analytic Hierarchy ◽  
Priority Vector ◽  
Judgment Error ◽  
Scale Error ◽  
The Analytic Hierarchy Process ◽  
Hierarchy Process

The Analytic Hierarchy Process (AHP) uses pairwise comparison to evaluate alternatives' advantages to a certain criterion. For decision-making problem with many different criteria and alternatives, pairwise comparison causes a prolonged decision-making period and rises fatigue in decision-makers' mentality. A question of practical value is if there exists a way to reduce judgment number and what influence the reduction will have on the overall evaluation of alternative ratings. To answer this question, we introduce scale error and judgment error into AHP judgment matrix. By expanding the scales defined in the AHP, scale error is eliminated. Taking judgment error as random variable, a new estimator to calculate priority vector is presented. In the end, an example is proved to show lowering judgment number will increase the probability of larger errors appearing in priority vector computation.

The Problem of Adequacy of the Analytic Hierarchy Process

2020 ◽  
Vol 10 (4) ◽  
pp. 79-87
Author(s):  
V.M. Romanchuk
Keyword(s):  
Analytic Hierarchy Process ◽  
Pairwise Comparison ◽  
Measurement Procedure ◽  
Ahp Method ◽  
Calculation Algorithm ◽  
Analytic Hierarchy ◽  
Rating Method ◽  
Simple Measurement ◽  
The Analytic Hierarchy Process ◽  
Hierarchy Process

The Analytic hierarchy process (AHP) is a popular method for solving multi-criteria problems. However, the problem of the adequacy of the AHP method is not solved. Opponents of the Analytic hierarchy process believe that the AHP as a whole is erroneous and cannot be applied in practice. Proponents of the method believe that the disadvantages of the method are compensated by a simple measurement procedure. In this paper, a modification of the AHP method is proposed. A mathematical model of measurement is formulated, which contains a built-in mechanism for checking adequacy. moreover, the measurement method is preserved, and the calculation algorithm becomes even simpler. The fact is that the Analytic hierarchy process is based on the assumption that the scale of relations can be obtained by pairwise comparison using numerical judgments based on the absolute scale of numbers. Fechner’s psychophysical law is considered as a justification for the existence of the scale of relations. But there are not one, but two psychophysical laws. The existence of two psychophysical laws is a problem of psychophysics. This problem can be solved by the rating method. To overcome the disadvantages of the Analytic hierarchy process, it is also proposed to use the rating method. The use of the rating method makes it possible to use the fundamental scale of the AHP method. As an example, the problem is solved using the traditional AHP scale.

scholarly journals A Method of Assigning Weights Using a Ranking and Nonhierarchy Comparison

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Bangweon Song ◽  
Seokjoong Kang
Keyword(s):  
Analytic Hierarchy Process ◽  
Pairwise Comparison ◽  
Analytic Hierarchy ◽  
Single Level ◽  
Consistency Ratio ◽  
Whole Number ◽  
The Analytic Hierarchy Process ◽  
Hierarchy Process

The analytic hierarchy process (AHP) has advantages that the whole number of comparisons can be reduced via a hierarchy structure and the consistency of responses verified via a consistency ratio. However, at the same time, the AHP has disadvantages that values vary according to the form of hierarchy structure and it is difficult to maintain consistency itself among responses. If the number of comparisons can be reduced, a comparison within a single level is optimal, and if comparison can be made while the priority among entities is maintained, consistency may be automatically maintained. Thus, in this study, we propose a method of assigning weights, which applies hierarchy structure of AHP and pairwise comparison but complements the disadvantages of AHP. This method has advantages that the number of comparisons can be reduced and also consistency is automatically maintained via determination of priorities first on multiple entities and subsequent comparisons between entities with adjoined priorities.

scholarly journals APPLYING THE ANALYTIC HIERARCHY PROCESS TO OIL SANDS ENVIRONMENTAL COMPLIANCE RISK MANAGEMENT

2016 ◽  
Vol 8 (1) ◽  
Author(s):  
Izak Johannes Roux ◽  
Dr. Christos Makrigeorgis
Keyword(s):  
Analytic Hierarchy Process ◽  
Oil Sands ◽  
Pairwise Comparison ◽  
Environmental Compliance ◽  
Analytic Hierarchy ◽  
Pairwise Comparison Matrix ◽  
Comparison Matrix ◽  
Risk Criteria ◽  
The Analytic Hierarchy Process ◽  
Hierarchy Process

<p>In 2013, oil companies in Alberta, Canada invested $32 billion in new oil-sands projects.  Despite the size of this investment, there is a demonstrable deficiency in the uniformity and understanding of environmental legislation requirements that translate into increased project compliance risks. In this paper, we applied the Analytic Hierarchy Process (AHP) to develop a priority list of environmental regulatory compliance risk criteria for oil-sands projects.  AHP belongs to the family of multicriteria decision-making (MCDM) techniques that utilizes a pairwise comparison matrix solicited from subject matter experts (SMEs) in the field as input.  The overall methodology itself consisted of 4 phases: (1) identification of the initial list of N potential environmental compliance risk criteria and verification of these criteria via a pilot survey; (2) formation of a pairwise comparison survey in the form of an N(N-1)/2 comparison matrix based on the verified criteria; (3) administration of the pairwise comparison matrix to a sample of 16 industry-specific SME’s; and (4) the application of the AHP method using SuperDecisions as a tool on the collected sample to rank the identified risk criteria. Our demonstrated results can potentially inform Alberta oil sands industry leaders about the ranking and utility of specific compliance risks as understood by experts and enable a more focused environmental compliance action to help increase legislative and public trust.</p>

scholarly journals Comparison of AHP and a Utility-Based Theory Method for Selected Vertical and Horizontal Forest Structure Indicators in the Sustainability Assessment of Forest Management in the Sierra de Guadarrama National Park, Madrid Region

2018 ◽  
Vol 10 (11) ◽  
pp. 4101 ◽  
Author(s):  
Susana Martín-Fernández ◽  
Adrián Gómez-Serrano ◽  
Eugenio Martínez-Falero ◽  
Cristina Pascual
Keyword(s):  
Forest Management ◽  
Analytic Hierarchy Process ◽  
National Park ◽  
Utility Theory ◽  
Sustainability Assessment ◽  
Local Level ◽  
Pairwise Comparison ◽  
Analytic Hierarchy ◽  
The Analytic Hierarchy Process ◽  
Hierarchy Process

This paper compares two pairwise comparison methods, the analytic hierarchy process (AHP) and a utility theory based method (UTB method), for sustainability assessment in forest management at the local level. Six alternatives were ranked, corresponding to six different types of forest management in the Sierra de Guadarrama National Park in the Madrid Region in Spain. The methods were tested by postgraduate students enrolled in a “Decision Support Systems” course at Universidad Politécnica de Madrid. Three sustainability indicators were considered: structural diversity, timber yield, and amount of biomass. The utility theory based method was the first to be compared, which is implemented in the computer program SILVANET. For each pair of alternatives, the students were asked which one they considered to be more sustainable. In the case of the Analytic Hierarchy Process, the students compared the indicators and the alternatives for each indicator. The Spearman’s correlation coefficient indicated that there was no correlation between the rankings for most of the students. The results revealed that the convergence in opinion in the AHP method was higher than in the utility based method for a low number of participants, and distinguished the differences between the alternatives more accurately. However in the case of the UTB method, the participants considered sustainability as a whole and made a more context-based comparison.

A METHOD FOR IMPROVING THE CONSISTENCY OF JUDGEMENTS

2002 ◽  
Vol 10 (06) ◽  
pp. 677-686 ◽  
Author(s):  
M. T. LAMATA ◽  
J. I. PELAEZ
Keyword(s):  
Analytic Hierarchy Process ◽  
Decision Maker ◽  
Pairwise Comparison ◽  
Analytic Hierarchy ◽  
Alternative Method ◽  
Consistency Problem ◽  
The Analytic Hierarchy Process ◽  
Hierarchy Process

The Analytic Hierarchy Process provides the decision maker with a method for improving the consistency of pairwise comparison matrices. Although it is one of the most commonly used method it presents some disadvantages related generally with the consistency problem. The purpose of this paper is to provide an alternative method for improving consistency and show how it can be applied to pairwise comparison matrices. The contribution to this method and also its limitations are shown at the end.

scholarly journals LINEAR PROGRAMMING MODELS FOR ESTIMATING WEIGHTS IN ANALYTIC HIERARCHY PROCESS AND FOR OPTIMIZATION OF HUMAN RESOURCE ALLOCATION

2016 ◽  
Vol 8 (2) ◽  
Author(s):  
Gokulananda Patel ◽  
Godwin D Mjema ◽  
Kasio M Godwin
Keyword(s):  
Linear Programming ◽  
Analytic Hierarchy Process ◽  
Human Resource ◽  
Pairwise Comparison ◽  
Food Product ◽  
Analytic Hierarchy ◽  
Pairwise Comparison Matrix ◽  
Frame Work ◽  
The Analytic Hierarchy Process ◽  
Hierarchy Process

The Analytic Hierarchy Process (AHP) provides a way to rank the alternatives by deriving priorities. In this paper we used Linear Programming (LP) models to estimate the weights of a pairwise comparison matrix derived within the frame work of the Analytic Hierarchy Process. The priorities obtained for the alternatives served as the coefficients of the objective function of linear programming to optimize a human resource problem at Bakhresa Food Product Limited (BFPL).

Materials selection criteria weighting method using analytic hierarchy process (AHP) with simplest questionnaire and modifying method of inconsistent pairwise comparison matrix

2021 ◽  
pp. 146442072110399
Author(s):  
Won-Chol Yang ◽  
Jae-Bok Ri ◽  
Ji-Yon Yang ◽  
Ju-Song Kim
Keyword(s):  
Analytic Hierarchy Process ◽  
Selection Criteria ◽  
Pairwise Comparison ◽  
Hot Water ◽  
Materials Selection ◽  
Analytic Hierarchy ◽  
Pairwise Comparison Matrix ◽  
Comparison Matrix ◽  
The Analytic Hierarchy Process ◽  
Hierarchy Process

The analytic hierarchy process has been widely used to determine subjective weights of materials selection criteria in materials selection using multi-criteria decision-making. However, the analytic hierarchy process has some drawbacks: it is difficult to construct a pairwise comparison matrix and meet the consistency requirement. First, we propose a new simplest questionnaire to perform the pairwise comparison without confusion, conventionally and easily. Next, we propose an improved modifying method for inconsistent pairwise comparison matrix according to the following principles: (1) the elements of the reconstructed pairwise comparison matrix should be nine-point scales, (2) the number and modifying the amount of the modified elements should be as small as possible and (3) the deviation between the original and reconstructed pairwise comparison matrixes should be as small as possible. The outline of the proposed modifying method is as follows: (1) calculate the consistency ration decrements of all the pairwise comparison matrixes reconstructed by modifying every element of the original pairwise comparison matrix to the lower and upper adjacent nine-point scales and (2) find the element with the maximum consistency ratio decrement and modify it to the lower or upper adjacent scale. To illustrate the effectiveness, we apply the proposed methods to determine the criteria weights for selecting the best phase change material used in a solar domestic hot water system, and apply the proposed modifying method to some examples from the published papers, and compare the performances with some previous methods. The simplest questionnaire and improved modifying method help materials designers and engineers to apply the analytic hierarchy process method in materials design and optimization problems, much more actively.

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